关键词: 反问题, 单边退化抛物方程, Fichera条件, Gateaux导数, 收敛性

Abstract: We considered the convergence analysis problem of the inversion of the radiation coefficient of a one-sided degenerate parabolic equation by using known terminal observation data. Firstly, it was necessary to satisfy the Fichera condition for the one-sided degenerate parabolic equation to ensure the solvability of the problem. Secondly, we transformed the original inverse problem into an optimal control problem and found the optimal solution for the radiation coefficient through optimal control methods. Finally, by combining the Gateaux derivative and introducing new source conditions, we proved the convergence of the optimal solution.

Key words: inverse problem, one-sided degenerate parabolic equation, Fichera condition, Gateaux derivative, convergence